What are you getting out of this relationship now?.
Did you yourself see heavily drinking parents as a child?. What drew you to this man in the first place let alone have children by him?. You modified your behaviour and changed; he has not fundamentally changed in all the years you've known him. You cannot act as a rescuer or saviour here to him and what you have tried to date (and you have not mentioned leaving him) has not worked.
Like many alcoholics as well he is selfishness personified. His primary relationship is with drink, its not with you or your kids.
Do you really love him or are you really confusing this with codependency?. His needs here are NOT more important than yours. You're really as caught up in his alcoholism as he is and your own recovery from this will only properly start when you are away from him.
Your family home as it is now is akin to a warzone; its certainly no sanctuary for you and your kids. Its not stable in your house either because you're merely going from one crisis situation into another. He is no father to them and you personally would be better off apart. He will no longer have you to prop him up and you should not enable him any longer. Life will NEVER be calm and happy so long as you and he are together for really your own reasons.
What do you want your children to learn about relationships and what are they learning here from you two as their parents?.
What do you want your kids to remember about their childhoods?. They are really having a shit time of it now and you're not helping any because your finite reserves of energy is being wasted on this manipulative person you call your partner. On an emotional level at least you are not fully available to your kids here. You're basically doing the same old roles that many people with alcoholics find themselves in; those of codependent partner, enabler and provoker. You will merely continue to go around and around in circles with him if you carry on like this. Doing the same in the hopes of expecting a different result is not going to work.
Many alcoholics self medicate with alcohol and his counsellor is also doing their bit here to enable him further. Get off the merry go around before you and your kids are further dragged down by him.
You need to get off the merry go around that is alcoholism altogether before you and your children are further dragged down by him. Pu your own selves first. You can only help your own self ultimately and you are not responsible for this man nor his choices. So the hell what that he does not have enough money to get a room elsewhere; where he goes is not your problem. See what I mean here about being codependent?. That is itself a problem. No obstacle to leaving is ultimately insurmountable and the issue of the mortgage can be dealt with.
Please contact Al-anon because it will help you. You will meet ordinary people just like you at those meetings. At the very least call them and read their literature.